{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Quantile Regression"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Quantile Regression is estimating either the condintional median or other quantiles of the response variable. This regression is used for when outliers, high skeweness and heteroscedasticity exist in the data. However, quantile regression predicts a quantile (or percentile) for a given indpedent variables.\n",
        "\n",
        "\n",
        "    1. Quite beneficial when heteroscedasticity is present in the data.\n",
        "    2. Robust to outliers\n",
        "    3. Distribution of dependent variable can be described via various quantiles.\n",
        "    5. It is more useful than linear regression when the data is skewed.\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "\n",
        "# fix_yahoo_finance is used to fetch data \n",
        "import fix_yahoo_finance as yf\n",
        "yf.pdr_override()"
      ],
      "outputs": [],
      "execution_count": 1,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# input\n",
        "symbol = 'AMD'\n",
        "start = '2014-01-01'\n",
        "end = '2018-08-27'\n",
        "\n",
        "# Read data \n",
        "dataset = yf.download(symbol,start,end)\n",
        "\n",
        "# View Columns\n",
        "dataset.head()"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[*********************100%***********************]  1 of 1 downloaded\n"
          ]
        },
        {
          "output_type": "execute_result",
          "execution_count": 2,
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Open</th>\n",
              "      <th>High</th>\n",
              "      <th>Low</th>\n",
              "      <th>Close</th>\n",
              "      <th>Adj Close</th>\n",
              "      <th>Volume</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Date</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2014-01-02</th>\n",
              "      <td>3.85</td>\n",
              "      <td>3.98</td>\n",
              "      <td>3.84</td>\n",
              "      <td>3.95</td>\n",
              "      <td>3.95</td>\n",
              "      <td>20548400</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2014-01-03</th>\n",
              "      <td>3.98</td>\n",
              "      <td>4.00</td>\n",
              "      <td>3.88</td>\n",
              "      <td>4.00</td>\n",
              "      <td>4.00</td>\n",
              "      <td>22887200</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2014-01-06</th>\n",
              "      <td>4.01</td>\n",
              "      <td>4.18</td>\n",
              "      <td>3.99</td>\n",
              "      <td>4.13</td>\n",
              "      <td>4.13</td>\n",
              "      <td>42398300</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2014-01-07</th>\n",
              "      <td>4.19</td>\n",
              "      <td>4.25</td>\n",
              "      <td>4.11</td>\n",
              "      <td>4.18</td>\n",
              "      <td>4.18</td>\n",
              "      <td>42932100</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2014-01-08</th>\n",
              "      <td>4.23</td>\n",
              "      <td>4.26</td>\n",
              "      <td>4.14</td>\n",
              "      <td>4.18</td>\n",
              "      <td>4.18</td>\n",
              "      <td>30678700</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "            Open  High   Low  Close  Adj Close    Volume\n",
              "Date                                                    \n",
              "2014-01-02  3.85  3.98  3.84   3.95       3.95  20548400\n",
              "2014-01-03  3.98  4.00  3.88   4.00       4.00  22887200\n",
              "2014-01-06  4.01  4.18  3.99   4.13       4.13  42398300\n",
              "2014-01-07  4.19  4.25  4.11   4.18       4.18  42932100\n",
              "2014-01-08  4.23  4.26  4.14   4.18       4.18  30678700"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 2,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X = dataset['Open']\n",
        "Y = dataset['Adj Close']"
      ],
      "outputs": [],
      "execution_count": 21,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from statsmodels.regression.quantile_regression import QuantReg\n",
        "import statsmodels.formula.api as smf"
      ],
      "outputs": [],
      "execution_count": 4,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "quant = QuantReg(X, Y)"
      ],
      "outputs": [],
      "execution_count": 22,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "for q in np.linspace(0.05, 0.95, 10):\n",
        "    print(q)\n",
        "    print(quant.fit(q=q).summary())\n",
        "    print()\n",
        "    print()"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.05\n",
            "                         QuantReg Regression Results                          \n",
            "==============================================================================\n",
            "Dep. Variable:                   Open   Pseudo R-squared:               0.9125\n",
            "Model:                       QuantReg   Bandwidth:                      0.1199\n",
            "Method:                 Least Squares   Sparsity:                        1.224\n",
            "Date:                Tue, 16 Oct 2018   No. Observations:                 1172\n",
            "Time:                        16:14:01   Df Residuals:                     1171\n",
            "                                        Df Model:                            1\n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Adj Close      0.9521      0.001   1012.933      0.000       0.950       0.954\n",
            "==============================================================================\n",
            "\n",
            "\n",
            "0.15\n",
            "                         QuantReg Regression Results                          \n",
            "==============================================================================\n",
            "Dep. Variable:                   Open   Pseudo R-squared:               0.9387\n",
            "Model:                       QuantReg   Bandwidth:                     0.06405\n",
            "Method:                 Least Squares   Sparsity:                       0.4956\n",
            "Date:                Tue, 16 Oct 2018   No. Observations:                 1172\n",
            "Time:                        16:14:01   Df Residuals:                     1171\n",
            "                                        Df Model:                            1\n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Adj Close      0.9749      0.001   1550.720      0.000       0.974       0.976\n",
            "==============================================================================\n",
            "\n",
            "\n",
            "0.25\n",
            "                         QuantReg Regression Results                          \n",
            "==============================================================================\n",
            "Dep. Variable:                   Open   Pseudo R-squared:               0.9497\n",
            "Model:                       QuantReg   Bandwidth:                     0.05545\n",
            "Method:                 Least Squares   Sparsity:                       0.3530\n",
            "Date:                Tue, 16 Oct 2018   No. Observations:                 1172\n",
            "Time:                        16:14:01   Df Residuals:                     1171\n",
            "                                        Df Model:                            1\n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Adj Close      0.9847      0.001   1861.431      0.000       0.984       0.986\n",
            "==============================================================================\n",
            "\n",
            "\n",
            "0.35\n",
            "                         QuantReg Regression Results                          \n",
            "==============================================================================\n",
            "Dep. Variable:                   Open   Pseudo R-squared:               0.9572\n",
            "Model:                       QuantReg   Bandwidth:                     0.05242\n",
            "Method:                 Least Squares   Sparsity:                       0.2852\n",
            "Date:                Tue, 16 Oct 2018   No. Observations:                 1172\n",
            "Time:                        16:14:01   Df Residuals:                     1171\n",
            "                                        Df Model:                            1\n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Adj Close      0.9911      0.000   2110.901      0.000       0.990       0.992\n",
            "==============================================================================\n",
            "\n",
            "\n",
            "0.44999999999999996\n",
            "                         QuantReg Regression Results                          \n",
            "==============================================================================\n",
            "Dep. Variable:                   Open   Pseudo R-squared:               0.9621\n",
            "Model:                       QuantReg   Bandwidth:                     0.05269\n",
            "Method:                 Least Squares   Sparsity:                       0.2726\n",
            "Date:                Tue, 16 Oct 2018   No. Observations:                 1172\n",
            "Time:                        16:14:01   Df Residuals:                     1171\n",
            "                                        Df Model:                            1\n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Adj Close      0.9973      0.000   2146.381      0.000       0.996       0.998\n",
            "==============================================================================\n",
            "\n",
            "\n",
            "0.5499999999999999\n",
            "                         QuantReg Regression Results                          \n",
            "==============================================================================\n",
            "Dep. Variable:                   Open   Pseudo R-squared:               0.9666\n",
            "Model:                       QuantReg   Bandwidth:                     0.05593\n",
            "Method:                 Least Squares   Sparsity:                       0.2650\n",
            "Date:                Tue, 16 Oct 2018   No. Observations:                 1172\n",
            "Time:                        16:14:01   Df Residuals:                     1171\n",
            "                                        Df Model:                            1\n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Adj Close      1.0024      0.000   2235.209      0.000       1.002       1.003\n",
            "==============================================================================\n",
            "\n",
            "\n",
            "0.65\n",
            "                         QuantReg Regression Results                          \n",
            "==============================================================================\n",
            "Dep. Variable:                   Open   Pseudo R-squared:               0.9676\n",
            "Model:                       QuantReg   Bandwidth:                     0.05568\n",
            "Method:                 Least Squares   Sparsity:                       0.2804\n",
            "Date:                Tue, 16 Oct 2018   No. Observations:                 1172\n",
            "Time:                        16:14:01   Df Residuals:                     1171\n",
            "                                        Df Model:                            1\n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Adj Close      1.0083      0.000   2232.166      0.000       1.007       1.009\n",
            "==============================================================================\n",
            "\n",
            "\n",
            "0.75\n",
            "                         QuantReg Regression Results                          \n",
            "==============================================================================\n",
            "Dep. Variable:                   Open   Pseudo R-squared:               0.9652\n",
            "Model:                       QuantReg   Bandwidth:                     0.05725\n",
            "Method:                 Least Squares   Sparsity:                       0.3430\n",
            "Date:                Tue, 16 Oct 2018   No. Observations:                 1172\n",
            "Time:                        16:14:01   Df Residuals:                     1171\n",
            "                                        Df Model:                            1\n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Adj Close      1.0156      0.001   2018.731      0.000       1.015       1.017\n",
            "==============================================================================\n",
            "\n",
            "\n",
            "0.85\n",
            "                         QuantReg Regression Results                          \n",
            "==============================================================================\n",
            "Dep. Variable:                   Open   Pseudo R-squared:               0.9624\n",
            "Model:                       QuantReg   Bandwidth:                     0.06966\n",
            "Method:                 Least Squares   Sparsity:                       0.4854\n",
            "Date:                Tue, 16 Oct 2018   No. Observations:                 1172\n",
            "Time:                        16:14:01   Df Residuals:                     1171\n",
            "                                        Df Model:                            1\n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Adj Close      1.0263      0.001   1747.975      0.000       1.025       1.027\n",
            "==============================================================================\n",
            "\n",
            "\n",
            "0.95\n",
            "                         QuantReg Regression Results                          \n",
            "==============================================================================\n",
            "Dep. Variable:                   Open   Pseudo R-squared:               0.9594\n",
            "Model:                       QuantReg   Bandwidth:                      0.1083\n",
            "Method:                 Least Squares   Sparsity:                       0.9807\n",
            "Date:                Tue, 16 Oct 2018   No. Observations:                 1172\n",
            "Time:                        16:14:01   Df Residuals:                     1171\n",
            "                                        Df Model:                            1\n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Adj Close      1.0440      0.001   1418.327      0.000       1.043       1.045\n",
            "==============================================================================\n",
            "\n",
            "\n"
          ]
        }
      ],
      "execution_count": 6,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mod = smf.quantreg('Close ~ Open + High + Low', dataset)\n",
        "res = mod.fit(q=.5)\n",
        "res.summary()"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 11,
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>QuantReg Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>       <td>Close</td>      <th>  Pseudo R-squared:  </th> <td>  0.9846</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>             <td>QuantReg</td>     <th>  Bandwidth:         </th> <td> 0.02332</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>          <td>Least Squares</td>  <th>  Sparsity:          </th> <td>  0.1217</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Tue, 16 Oct 2018</td> <th>  No. Observations:  </th>  <td>  1172</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>16:14:44</td>     <th>  Df Residuals:      </th>  <td>  1168</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th> </th>                      <td> </td>        <th>  Df Model:          </th>  <td>     3</td> \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Intercept</th> <td>   -0.0061</td> <td>    0.003</td> <td>   -1.950</td> <td> 0.051</td> <td>   -0.012</td> <td>  3.8e-05</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Open</th>      <td>   -0.6172</td> <td>    0.013</td> <td>  -47.655</td> <td> 0.000</td> <td>   -0.643</td> <td>   -0.592</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>High</th>      <td>    0.8462</td> <td>    0.012</td> <td>   72.067</td> <td> 0.000</td> <td>    0.823</td> <td>    0.869</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Low</th>       <td>    0.7706</td> <td>    0.012</td> <td>   62.130</td> <td> 0.000</td> <td>    0.746</td> <td>    0.795</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                         QuantReg Regression Results                          \n",
              "==============================================================================\n",
              "Dep. Variable:                  Close   Pseudo R-squared:               0.9846\n",
              "Model:                       QuantReg   Bandwidth:                     0.02332\n",
              "Method:                 Least Squares   Sparsity:                       0.1217\n",
              "Date:                Tue, 16 Oct 2018   No. Observations:                 1172\n",
              "Time:                        16:14:44   Df Residuals:                     1168\n",
              "                                        Df Model:                            3\n",
              "==============================================================================\n",
              "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "Intercept     -0.0061      0.003     -1.950      0.051      -0.012     3.8e-05\n",
              "Open          -0.6172      0.013    -47.655      0.000      -0.643      -0.592\n",
              "High           0.8462      0.012     72.067      0.000       0.823       0.869\n",
              "Low            0.7706      0.012     62.130      0.000       0.746       0.795\n",
              "==============================================================================\n",
              "\"\"\""
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 11,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X = np.array(dataset['Open'], dtype=np.float64)\n",
        "Y = np.array(dataset['Adj Close'], dtype=np.float64)"
      ],
      "outputs": [],
      "execution_count": 28,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "res = QuantReg(Y, X).fit(0.5, bandwidth='chamberlain')\n",
        "res.summary()"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 29,
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>QuantReg Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>         <td>y</td>        <th>  Pseudo R-squared:  </th> <td>  0.9646</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>             <td>QuantReg</td>     <th>  Bandwidth:         </th> <td> 0.01715</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>          <td>Least Squares</td>  <th>  Sparsity:          </th> <td>  0.2686</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Tue, 16 Oct 2018</td> <th>  No. Observations:  </th>  <td>  1172</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>16:42:46</td>     <th>  Df Residuals:      </th>  <td>  1171</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th> </th>                      <td> </td>        <th>  Df Model:          </th>  <td>     1</td> \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x1</th> <td>    1.0000</td> <td>    0.000</td> <td> 2177.970</td> <td> 0.000</td> <td>    0.999</td> <td>    1.001</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                         QuantReg Regression Results                          \n",
              "==============================================================================\n",
              "Dep. Variable:                      y   Pseudo R-squared:               0.9646\n",
              "Model:                       QuantReg   Bandwidth:                     0.01715\n",
              "Method:                 Least Squares   Sparsity:                       0.2686\n",
              "Date:                Tue, 16 Oct 2018   No. Observations:                 1172\n",
              "Time:                        16:42:46   Df Residuals:                     1171\n",
              "                                        Df Model:                            1\n",
              "==============================================================================\n",
              "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "x1             1.0000      0.000   2177.970      0.000       0.999       1.001\n",
              "==============================================================================\n",
              "\"\"\""
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 29,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"estimated coefficients: \", res.params) "
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "estimated coefficients:  [0.99999905]\n"
          ]
        }
      ],
      "execution_count": 56,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "predictions = res.predict(Y)\n",
        "predictions"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 57,
          "data": {
            "text/plain": [
              "array([ 3.94999625,  3.99999621,  4.12999608, ..., 22.28997986,\n",
              "       23.97997725, 25.25997604])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 57,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(X,Y)\n",
        "plt.plot(predictions)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 58,
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x186775ffd30>]"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": [
              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\n"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 58,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(X, predictions, color='g')"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 59,
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x1867760f7f0>]"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": [
              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\n"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 59,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mod = smf.quantreg('Close ~ Open', dataset)\n",
        "res = mod.fit(q=.5)\n",
        "res.summary()\n",
        "\n",
        "quantiles = np.arange(.05, .96, .1)\n",
        "def fit_model(q):\n",
        "    res = mod.fit(q=q)\n",
        "    return [q, res.params['Intercept'], res.params['Open']] + \\\n",
        "            res.conf_int().loc['Open'].tolist()\n",
        "    \n",
        "models = [fit_model(x) for x in quantiles]\n",
        "models = pd.DataFrame(models, columns=['q', 'a', 'b','lb','ub'])\n",
        "\n",
        "ols = smf.ols('Close ~ Open', dataset).fit()\n",
        "ols_ci = ols.conf_int().loc['Open'].tolist()\n",
        "ols = dict(a = ols.params['Intercept'],\n",
        "           b = ols.params['Open'],\n",
        "           lb = ols_ci[0],\n",
        "           ub = ols_ci[1])\n",
        "\n",
        "print(models)\n",
        "print(ols)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "      q         a         b        lb        ub\n",
            "0  0.05  0.001422  0.956459  0.953780  0.959138\n",
            "1  0.15  0.002624  0.973185  0.971156  0.975214\n",
            "2  0.25 -0.001128  0.983687  0.981911  0.985463\n",
            "3  0.35 -0.000974  0.991150  0.989577  0.992724\n",
            "4  0.45 -0.005219  0.997903  0.996358  0.999449\n",
            "5  0.55  0.001193  1.002294  1.000702  1.003885\n",
            "6  0.65 -0.002310  1.008613  1.007020  1.010207\n",
            "7  0.75  0.004935  1.013916  1.012101  1.015731\n",
            "8  0.85 -0.002257  1.025515  1.023353  1.027678\n",
            "9  0.95  0.017680  1.045930  1.041683  1.050177\n",
            "{'a': 4.270073805337504e-05, 'b': 1.0002530247743395, 'lb': 0.9974880736735984, 'ub': 1.0030179758750808}\n"
          ]
        }
      ],
      "execution_count": 66,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = np.arange(dataset.Open.min(), dataset.Open.max(), 20)\n",
        "get_y = lambda a, b: a + b * x\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(8, 6))\n",
        "\n",
        "for i in range(models.shape[0]):\n",
        "    y = get_y(models.a[i], models.b[i])\n",
        "    ax.plot(x, y, linestyle='dotted', color='grey')\n",
        "    \n",
        "y = get_y(ols['a'], ols['b'])\n",
        "\n",
        "ax.plot(x, y, color='red', label='OLS')\n",
        "ax.scatter(dataset.Open, dataset.Close, alpha=.2)\n",
        "ax.set_xlim((1, 24))\n",
        "ax.set_ylim((1, 24))\n",
        "legend = ax.legend()\n",
        "ax.set_xlabel('Open', fontsize=16)\n",
        "ax.set_ylabel('Close', fontsize=16);"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": [
              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\n"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 77,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "n = models.shape[0]\n",
        "p1 = plt.plot(models.q, models.b, color='black', label='Quantile Reg.')\n",
        "p2 = plt.plot(models.q, models.ub, linestyle='dotted', color='black')\n",
        "p3 = plt.plot(models.q, models.lb, linestyle='dotted', color='black')\n",
        "p4 = plt.plot(models.q, [ols['b']] * n, color='red', label='OLS')\n",
        "p5 = plt.plot(models.q, [ols['lb']] * n, linestyle='dotted', color='red')\n",
        "p6 = plt.plot(models.q, [ols['ub']] * n, linestyle='dotted', color='red')\n",
        "plt.ylabel(r'$\\beta_{Open}$')\n",
        "plt.xlabel('Quantiles of the conditional Close distribution')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": [
              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\n"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 78,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    }
  ],
  "metadata": {
    "kernel_info": {
      "name": "python3"
    },
    "language_info": {
      "mimetype": "text/x-python",
      "name": "python",
      "file_extension": ".py",
      "version": "3.5.5",
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3"
    },
    "kernelspec": {
      "name": "python3",
      "language": "python",
      "display_name": "Python 3"
    },
    "nteract": {
      "version": "0.23.1"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 4
}